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A prestressed elastic medium containing a mode-III crack is studied by means of the couple stress theory (CST). Based on the CST under initial stresses, a governing differential equation along with a mixed boundary value problem is established. The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method. To determine their intensity, a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial. The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor (CSIF) and the force stress intensity factor (FSIF) around the crack tips. The symmetric part of the shear stress has no singularity, and the skew-symmetric part related to the couple stress exhibits an r−3/2 singularity, in which r is the distance from the crack tip. The initial stresses also affect the crack tearing displacement and the CSIF and FSIF. [ABSTRACT FROM AUTHOR]

In this work, the three-dimensional (3D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated. The analytical solutions of the fundamental wave and second harmonic with the quasi-longitudinal (qP) and quasi-shear (qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem. The transmission coefficients are calculated to support the band gap property, and the tunability of the nonreciprocal transmission by the initial stress is discussed. This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics. [ABSTRACT FROM AUTHOR]

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables. [ABSTRACT FROM AUTHOR]

The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices. [ABSTRACT FROM AUTHOR]

The present study is carried out to investigate the transference of torsional surface waves in a heterogeneous anisotropic crust lying over a dry sandy half-space. The rigidities and densities as well as the initial stress are assumed varying as a function of depth in both the media. These variations are the product of the polynomial function of depth in degree n (n ∈ ℝ) and the exponential function of depth. Following the theory of elastic waves, the mathematical model is established. Separation of variables is used to obtain the displacement in the layer and the half-space. Intrinsic boundary conditions are imposed to derive the dispersion equation. The inhomogeneity parameters associated with the rigidity, the density, and the initial stress of the medium are found to have substantial influence on the phase velocity of the torsional surface wave. The graphical presentations are drawn to exhibit the findings. The results thus obtained are significant for the investigation and characterization of torsional surface wave in the heterogeneous anisotropic layer. [ABSTRACT FROM AUTHOR]

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman (L-S) model and the dual-phase-lag (DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material. [ABSTRACT FROM AUTHOR]

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano's and Ferrari's methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically. [ABSTRACT FROM AUTHOR]

Propagation of a torsional wave in a doubly-layered half-space structure of an initially stressed heterogeneous viscoelastic layer sandwiched between a layer and a half-space of heterogeneous dry sandy media is studied. A closed form complex expression for the velocity profile is obtained under effective boundary conditions. The real part of the complex expression provides a dispersion equation, and the imaginary part yields a damping equation. The derived dispersion and damped equations are in well agreement with the classical Love wave condition. In addition, to study the effect of the dissipation factor, the attenuation coefficient, the sandy parameters, the initial stress, the heterogeneity parameters, and the thickness ratio parameter, some noteworthy contemplations are made by numerical calculations and graphical visuals. The results of this paper may present a deeper insight into the behaviour of propagation phenomena in heterogeneous viscoelastic and heterogeneous dry sandy materials that can provide a theoretical guide for the design and optimization in the field of earthquake engineering. The study also reveals that the presence of a damping part due to viscoelasticity affects the torsional wave propagation significantly. [ABSTRACT FROM AUTHOR]

In this paper, we present an analytical method for evaluating the stress field within a casing-cement-formation system of oil/gas wells under anisotropic in-situ stresses in the rock formation and uniform pressure within the casing. The present method treats the in-situ stresses in the formation as initial stresses since the in-situ stresses have already developed in the formation before placement of cement and casing into the well. It is demonstrated that, via this treatment, the present method excludes additional displacements within the formation predicted by the existing method, and gives more reasonable stress results. An actual tight-oil well is analyzed using the present and existing analytical methods, as well as the finite element method. Good agreement between the analytical results and the finite element analysis (FEA) results is obtained, validating the present method. It is also evident that, compared with the present method, the existing method overestimates the compressive stress level within the casing and the cement. Finally, the effects of elastic properties of the formation, cement, and inner pressure of casing on stresses within the casing and cement are illustrated with a series of sensitivity analyses. [ABSTRACT FROM AUTHOR]

The present paper contributes in studying the phase velocities of P- and S-waves in a half space subjected to a compressive initial stress and gravity field. The density and acceleration due to gravity vary quadratically along the depth. The dispersion equation is derived in a closed form. It is shown that the phase velocities depend not only on the initial stress, gravity, and direction of propagation but also on the inhomogeneity parameter associated with the density and acceleration due to gravity. Various particular cases are obtained, and the results match with the classical results. Numerical investigations on the phase velocities of P- and S-waves against the wave number are made for various sets of values of the material parameters, and the results are illustrated graphically. The graphical user interface model is developed to generalize the effect. [ABSTRACT FROM AUTHOR]

The paper studies the propagation of Love waves in a non-homogeneous substratum over an initially stressed heterogeneous half-space. The dispersion equation of phase velocity is derived. The velocities of Love waves are calculated numerically as a function of kH and presented in a number of graphs, where k is the wave number, and H is the thickness of the layer. The case of Gibson's half-space is also considered. It is observed that the speed of Love waves is finite in the vicinity of the surface of the half-space and vanishes as the depth increases for a particular wave number. It is also observed that an increase in compressive initial stresses causes decreases of Love waves velocity for the same frequency, and the tensile initial stress of small magnitude in the half-space causes increase of the velocity. [ABSTRACT FROM AUTHOR]

The paper studies the propagation of torsional surface waves in an initially stressed anisotropic poro-elastic layer over a semi-infinite heterogeneous half space with linearly varying rigidity and density due to irregularity at the interface. The irregularity is taken in the half space in the form of a rectangle. It is observed that torsional surface waves propagate in this assumed medium. In the absence of the irregularity, the velocity equation of the torsional surface wave is also obtained. For a layer over a homogeneous half space, the velocity of torsional surface waves coincides with that of the Love waves. [ABSTRACT FROM AUTHOR]

A theoretical analysis of the lateral resonances in 1–3 piezocomposites with poling initial stress is conducted using the Bloch wave theory. Based on the linear piezoelectricity theory, theoretical formulations that include initial stress for the propagation of acoustic plane waves are made. Numerical calculations are performed to study the effects of the initial stress on the lateral mode frequencies and the stop band. It is found that lateral mode frequencies increase with the piezoelectricity of the piezocomposites, but decrease with the poling initial stress. The influence of the initial shear stress on the lateral mode frequencies is minimal, and can thus be neglected. [ABSTRACT FROM AUTHOR]